Background: Meta-analysis is used to combine evidence from relevant studies in systematic reviews. However, the evidential value of the observed result is not properly evaluated because most statistical analyses are conducted and presented in terms of a frequentist paradigm. This is a fundamentally flawed approach because it attempts to measure evidence using data that was not observed. Once a study is conducted and the results are known, the probability distribution of the outcome scores remains a function (the likelihood function (LF)) of the unknown parameters only. We focus on using the LF to measure the relative support (evidence) the observed data provides to various hypotheses (parameter values) in single treatment arms.

Objectives: To illustrate how the evidential value within each arm of both the single and multiple studies can be evaluated using a likelihood approach (LA); focusing on descriptive inference of rare harmful events. Methods and Results: The risk, within and across studies, and the heterogeneity of the risk between studies are evaluated assuming binomial and beta-binomial distributions. Point estimation is determined by computing the most supported value (MSV). Interval estimation is determined by pre-specifying a minimally acceptable 'level of support’ and deriving the respective support interval (SI) from the LF. Computations and graphing of the LF were implemented in R. Point hypotheses can be naturally tested and we discuss approaches to testing composite hypotheses. We compare the results with the standard frequentist analysis.

Conclusions: The likelihood approach is a better justified approach to evaluating the evidence from data. The interpretation of the LF provides a relevant meaning to the point and interval estimates as well as a more intuitive way to select the width of the interval. It provides superior intervals, when there are few or no events. However there are computational challenges to overcome.